Bandgap voltage reference circuits are well known in the art. Such circuits are designed to sum two voltages with opposite temperature slopes. One of the voltages is a Complementary-To-Absolute Temperature (CTAT) voltage typically provided by a base-emitter voltage of a forward biased bipolar transistor. The other is a Proportional-To-Absolute Temperature (PTAT) voltage typically derived from the base-emitter voltage differences of two bipolar transistors operating at different collector current densities. When the PTAT voltage and the CTAT voltage are summed together the summed voltage is at a first order temperature insensitive. The voltage reference signals provided by bandgap voltage reference circuits known heretofore require curvature correction due to the non-linearity of base-emitter voltage as explained below. The base-emitter voltage of a bipolar transistor is temperature dependent and can be defined by equation (1).
                                          V            be                    ⁡                      (            T            )                          =                                            V                              G                ⁢                                                                  ⁢                0                                      ⁡                          (                              1                -                                  T                                      T                    0                                                              )                                +                                                    V                be                            ⁡                              (                                  T                  0                                )                                      *                          T                              T                0                                              -                      X            ⁢                                                  ⁢            T            ⁢                                                  ⁢            I            *                          V                              T                ⁢                                                                  ⁢                0                                      *                          T                              T                0                                      *                          ln              ⁡                              (                                  T                                      T                    0                                                  )                                              +                                    V                              T                ⁢                                                                  ⁢                0                                      *                          T                              T                0                                      *                          ln              ⁡                              (                                                      Ic                    ⁡                                          (                      T                      )                                                                            Ic                    ⁡                                          (                                              T                        0                                            )                                                                      )                                                                        (        1        )            Where:                Vbe(T) is base-emitter voltage at actual temperature, T,        Vbe0 is base-emitter voltage at temperature T0 (˜0.65V at T0=300K),        VG0 is extrapolated bandgap voltage at 0K (˜1.14V),        XTI corresponds to saturation current temperature exponent (˜3 to 5),        VT0 is thermal voltage at temperature T0 (˜25.8 mV at T0=300K).        
The collector currents of bipolar transistors correspond to a ratio of a voltage, VR, (PTAT, CTAT, constant or combinations) over a resistor, R. The resistor is also temperature dependent such that:
                                          Ic            ⁡                          (              T              )                                            Ic            ⁡                          (                              T                0                            )                                      ≈                              (                          T                              T                0                                      )                    c                                    (        2        )            
Temperature exponent, c, in equation (2) corresponds to temperature dependence of VR and resistor R.
Combining equation (1) and equation (2):
                                          V            be                    ⁡                      (            T            )                          =                                            V                              G                ⁢                                                                  ⁢                0                                      ⁡                          (                              1                -                                  T                                      T                    0                                                              )                                +                                                    V                be                            ⁡                              (                                  T                  0                                )                                      *                          T                              T                0                                              -                                    (                                                X                  ⁢                                                                          ⁢                  T                  ⁢                                                                          ⁢                  I                                -                c                            )                        *                          V                              T                ⁢                                                                  ⁢                0                                      *                          T                              T                0                                      *                          ln              ⁡                              (                                  T                                      T                    0                                                  )                                                                        (        3        )            
If voltage VR is PTAT and R has zero temperature coefficient (TC) then c=1. The last term in equation (3) corresponds to non-linearity of base-emitter voltage which is also reflected in the reference voltage since the PTAT voltage component of the reference voltage has very low non-linearity. When the reference voltage is trimmed for minimum TC this nonlinearity displays a voltage variation of the form of a “bow” or curve with maximum deviation in the middle of the industrial temperature range (−40° C. to 85° C.). For a reference voltage with nominal voltage of about 1.24V implemented in a submicron CMOS process maximum voltage deviation due to the nonlinear term is of the order of 2 mV to 5 mV. Accordingly for industrial temperature ranges (typically −40° C. to 85° C.) the TC cannot be reduced to less than 10 to 20 ppm/° C. without further curvature correction.
An example of a prior art bandgap voltage reference circuit 100 is illustrated in FIG. 1. This circuit is exemplary of the type of prior art circuitry which requires curvature correction. The bandgap voltage reference circuit 100 includes a first bipolar transistor 110 operating at first collector current density and a second bipolar transistor 115 operating at a second collector current density which is less than that of the first collector current density. The emitter of the first bipolar transistor 110 is coupled to the non-inverting terminal of an operational amplifier 118, and the emitter of the second bipolar transistor 115 is coupled via a resistor, r1, 122 to the inverting terminal of the amplifier 118. The collector current density difference may be established by having the emitter area of the second bipolar transistor 115 larger than the emitter area of the first bipolar transistor 110. Alternatively multiple transistors may be provided in each leg, with the sum of the collector currents of each of the transistors in a first leg being greater than that in a second leg. As a consequence of the differences in collector current densities between the transistors coupled to each of the legs of the amplifier, a base-emitter voltage difference (ΔVbe) is reflected across the resistor, r1, 122. This voltage difference is of the form of a proportional to absolute temperature (PTAT) voltage. Two PMOS transistor 130A, 130B provide bias current to the first and second bipolar transistors, respectively. If the two PMOS transistors 130A and 130B are assumed to be identical; the amplifier 118 is operable as an ideal amplifier and the base currents of the first bipolar transistor 110 and the second bipolar transistor 115 are negligible compared to the corresponding emitter and collector currents. The PTAT voltage developed across resistor r1, 122 is:
                              Δ          ⁢                                          ⁢                      V            be                          =                              V                          T              ⁢                                                          ⁢              0                                *                      T                          T              0                                *                      ln            ⁡                          (              n              )                                                          (        4        )            
The reference voltage at the output node 140 corresponds to base-emitter voltage of the first bipolar device 110 plus the base-emitter voltage difference ΔVbe scaled by the ratio of resistor 122 and a feedback resistor, r2, 133 coupled to the inverting terminal of the amplifier 118 and the output node 140.
                              V          ref                =                              V            be                    +                      Δ            ⁢                                                  ⁢                          V              be                        *                                          r                ⁢                                                                  ⁢                1                                            r                ⁢                                                                  ⁢                2                                                                        (        5        )            
As the collector currents of the first and second bipolar transistors are PTAT the coefficient “c” in equation (3) is one and the non-linear component of the form of T log T is scaled by the factor of XTI-1. Different correction methods are used to compensate for nonlinearity of the form of T log T in bandgap voltage references.
Known correction methods introduce an inverse curvature on base-emitter voltage difference of suitable magnitude such that when they are combined to generate the reference voltage, the two pairs of linear and nonlinear voltage components compensate for each other. In order to apply such a signal, the bipolar transistors 110, 115 which generate the bandgap voltage reference are biased with different currents. Typically, the bipolar transistor 115 operating at the lower collector current density is biased with constant current and the bipolar transistor 110 operating with high collector current density is biased with PTAT current. Different biasing circuits are used to generate the required constant current for biasing the bipolar transistor 110. Such biasing circuits typically require an extra amplifier and a large resistor to reflect across it a constant voltage or a CTAT voltage. When CTAT voltage is used a CTAT current is generated, and this current is added to a balanced PTAT current to generate a constant current.
While such circuitry provides for the necessary curvature compensation it does so at the expense of die area in that the components used, the additional amplifier and the large resistor typically occupy large areas on the die where the circuitry is provided.
There is therefore a need to provide a bandgap voltage reference that compensates for voltage reference curvature but does not require large area devices to achieve this compensation.